Dissipation and fluctuation of the relative momentum in nucleus-nucleus collisions

The dissipation of the relative momentum in nucleus-nucleus collisions is treated in terms of a Langevin equation with a fluctuating force. Equations of motion for first and second moments of the macroscopic variables are derived directly from the Langevin equation. The properties of the fluctuating force which results from random particle exchange are investigated in detail. Drift and diffusion coefficients are calculated microscopically and analytical expressions are given which can be used in any trajectory calculation. An important feature of the model is that the Einstein relation between dissipation and fluctuation turns out to be only a limiting case of a more general expression which includes nonthermal fluctuations. By treating the two nuclei as intrinsically equilibrated but not in thermal equilibrium with respect to each other, several important aspects of the dissipative behaviour, seen in heavy-ion collisions with final energies above the Coulomb barrier, can be understood.